1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud (at) inria.fr> 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 #ifndef EIGEN_ALIGNEDBOX_H 11 #define EIGEN_ALIGNEDBOX_H 12 13 namespace Eigen { 14 15 /** \geometry_module \ingroup Geometry_Module 16 * 17 * 18 * \class AlignedBox 19 * 20 * \brief An axis aligned box 21 * 22 * \param _Scalar the type of the scalar coefficients 23 * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. 24 * 25 * This class represents an axis aligned box as a pair of the minimal and maximal corners. 26 */ 27 template <typename _Scalar, int _AmbientDim> 28 class AlignedBox 29 { 30 public: 31 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim) 32 enum { AmbientDimAtCompileTime = _AmbientDim }; 33 typedef _Scalar Scalar; 34 typedef NumTraits<Scalar> ScalarTraits; 35 typedef DenseIndex Index; 36 typedef typename ScalarTraits::Real RealScalar; 37 typedef typename ScalarTraits::NonInteger NonInteger; 38 typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType; 39 40 /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */ 41 enum CornerType 42 { 43 /** 1D names */ 44 Min=0, Max=1, 45 46 /** Added names for 2D */ 47 BottomLeft=0, BottomRight=1, 48 TopLeft=2, TopRight=3, 49 50 /** Added names for 3D */ 51 BottomLeftFloor=0, BottomRightFloor=1, 52 TopLeftFloor=2, TopRightFloor=3, 53 BottomLeftCeil=4, BottomRightCeil=5, 54 TopLeftCeil=6, TopRightCeil=7 55 }; 56 57 58 /** Default constructor initializing a null box. */ 59 inline AlignedBox() 60 { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); } 61 62 /** Constructs a null box with \a _dim the dimension of the ambient space. */ 63 inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim) 64 { setEmpty(); } 65 66 /** Constructs a box with extremities \a _min and \a _max. */ 67 template<typename OtherVectorType1, typename OtherVectorType2> 68 inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {} 69 70 /** Constructs a box containing a single point \a p. */ 71 template<typename Derived> 72 inline explicit AlignedBox(const MatrixBase<Derived>& a_p) 73 { 74 typename internal::nested<Derived,2>::type p(a_p.derived()); 75 m_min = p; 76 m_max = p; 77 } 78 79 ~AlignedBox() {} 80 81 /** \returns the dimension in which the box holds */ 82 inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); } 83 84 /** \deprecated use isEmpty */ 85 inline bool isNull() const { return isEmpty(); } 86 87 /** \deprecated use setEmpty */ 88 inline void setNull() { setEmpty(); } 89 90 /** \returns true if the box is empty. */ 91 inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); } 92 93 /** Makes \c *this an empty box. */ 94 inline void setEmpty() 95 { 96 m_min.setConstant( ScalarTraits::highest() ); 97 m_max.setConstant( ScalarTraits::lowest() ); 98 } 99 100 /** \returns the minimal corner */ 101 inline const VectorType& (min)() const { return m_min; } 102 /** \returns a non const reference to the minimal corner */ 103 inline VectorType& (min)() { return m_min; } 104 /** \returns the maximal corner */ 105 inline const VectorType& (max)() const { return m_max; } 106 /** \returns a non const reference to the maximal corner */ 107 inline VectorType& (max)() { return m_max; } 108 109 /** \returns the center of the box */ 110 inline const CwiseUnaryOp<internal::scalar_quotient1_op<Scalar>, 111 const CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> > 112 center() const 113 { return (m_min+m_max)/2; } 114 115 /** \returns the lengths of the sides of the bounding box. 116 * Note that this function does not get the same 117 * result for integral or floating scalar types: see 118 */ 119 inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> sizes() const 120 { return m_max - m_min; } 121 122 /** \returns the volume of the bounding box */ 123 inline Scalar volume() const 124 { return sizes().prod(); } 125 126 /** \returns an expression for the bounding box diagonal vector 127 * if the length of the diagonal is needed: diagonal().norm() 128 * will provide it. 129 */ 130 inline CwiseBinaryOp< internal::scalar_difference_op<Scalar>, const VectorType, const VectorType> diagonal() const 131 { return sizes(); } 132 133 /** \returns the vertex of the bounding box at the corner defined by 134 * the corner-id corner. It works only for a 1D, 2D or 3D bounding box. 135 * For 1D bounding boxes corners are named by 2 enum constants: 136 * BottomLeft and BottomRight. 137 * For 2D bounding boxes, corners are named by 4 enum constants: 138 * BottomLeft, BottomRight, TopLeft, TopRight. 139 * For 3D bounding boxes, the following names are added: 140 * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil. 141 */ 142 inline VectorType corner(CornerType corner) const 143 { 144 EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE); 145 146 VectorType res; 147 148 Index mult = 1; 149 for(Index d=0; d<dim(); ++d) 150 { 151 if( mult & corner ) res[d] = m_max[d]; 152 else res[d] = m_min[d]; 153 mult *= 2; 154 } 155 return res; 156 } 157 158 /** \returns a random point inside the bounding box sampled with 159 * a uniform distribution */ 160 inline VectorType sample() const 161 { 162 VectorType r; 163 for(Index d=0; d<dim(); ++d) 164 { 165 if(!ScalarTraits::IsInteger) 166 { 167 r[d] = m_min[d] + (m_max[d]-m_min[d]) 168 * internal::random<Scalar>(Scalar(0), Scalar(1)); 169 } 170 else 171 r[d] = internal::random(m_min[d], m_max[d]); 172 } 173 return r; 174 } 175 176 /** \returns true if the point \a p is inside the box \c *this. */ 177 template<typename Derived> 178 inline bool contains(const MatrixBase<Derived>& a_p) const 179 { 180 typename internal::nested<Derived,2>::type p(a_p.derived()); 181 return (m_min.array()<=p.array()).all() && (p.array()<=m_max.array()).all(); 182 } 183 184 /** \returns true if the box \a b is entirely inside the box \c *this. */ 185 inline bool contains(const AlignedBox& b) const 186 { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); } 187 188 /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this. */ 189 template<typename Derived> 190 inline AlignedBox& extend(const MatrixBase<Derived>& a_p) 191 { 192 typename internal::nested<Derived,2>::type p(a_p.derived()); 193 m_min = m_min.cwiseMin(p); 194 m_max = m_max.cwiseMax(p); 195 return *this; 196 } 197 198 /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this. */ 199 inline AlignedBox& extend(const AlignedBox& b) 200 { 201 m_min = m_min.cwiseMin(b.m_min); 202 m_max = m_max.cwiseMax(b.m_max); 203 return *this; 204 } 205 206 /** Clamps \c *this by the box \a b and returns a reference to \c *this. */ 207 inline AlignedBox& clamp(const AlignedBox& b) 208 { 209 m_min = m_min.cwiseMax(b.m_min); 210 m_max = m_max.cwiseMin(b.m_max); 211 return *this; 212 } 213 214 /** Returns an AlignedBox that is the intersection of \a b and \c *this */ 215 inline AlignedBox intersection(const AlignedBox& b) const 216 {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); } 217 218 /** Returns an AlignedBox that is the union of \a b and \c *this */ 219 inline AlignedBox merged(const AlignedBox& b) const 220 { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); } 221 222 /** Translate \c *this by the vector \a t and returns a reference to \c *this. */ 223 template<typename Derived> 224 inline AlignedBox& translate(const MatrixBase<Derived>& a_t) 225 { 226 const typename internal::nested<Derived,2>::type t(a_t.derived()); 227 m_min += t; 228 m_max += t; 229 return *this; 230 } 231 232 /** \returns the squared distance between the point \a p and the box \c *this, 233 * and zero if \a p is inside the box. 234 * \sa exteriorDistance() 235 */ 236 template<typename Derived> 237 inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& a_p) const; 238 239 /** \returns the squared distance between the boxes \a b and \c *this, 240 * and zero if the boxes intersect. 241 * \sa exteriorDistance() 242 */ 243 inline Scalar squaredExteriorDistance(const AlignedBox& b) const; 244 245 /** \returns the distance between the point \a p and the box \c *this, 246 * and zero if \a p is inside the box. 247 * \sa squaredExteriorDistance() 248 */ 249 template<typename Derived> 250 inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const 251 { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(p))); } 252 253 /** \returns the distance between the boxes \a b and \c *this, 254 * and zero if the boxes intersect. 255 * \sa squaredExteriorDistance() 256 */ 257 inline NonInteger exteriorDistance(const AlignedBox& b) const 258 { using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(b))); } 259 260 /** \returns \c *this with scalar type casted to \a NewScalarType 261 * 262 * Note that if \a NewScalarType is equal to the current scalar type of \c *this 263 * then this function smartly returns a const reference to \c *this. 264 */ 265 template<typename NewScalarType> 266 inline typename internal::cast_return_type<AlignedBox, 267 AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const 268 { 269 return typename internal::cast_return_type<AlignedBox, 270 AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this); 271 } 272 273 /** Copy constructor with scalar type conversion */ 274 template<typename OtherScalarType> 275 inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other) 276 { 277 m_min = (other.min)().template cast<Scalar>(); 278 m_max = (other.max)().template cast<Scalar>(); 279 } 280 281 /** \returns \c true if \c *this is approximately equal to \a other, within the precision 282 * determined by \a prec. 283 * 284 * \sa MatrixBase::isApprox() */ 285 bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const 286 { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); } 287 288 protected: 289 290 VectorType m_min, m_max; 291 }; 292 293 294 295 template<typename Scalar,int AmbientDim> 296 template<typename Derived> 297 inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const 298 { 299 typename internal::nested<Derived,2*AmbientDim>::type p(a_p.derived()); 300 Scalar dist2(0); 301 Scalar aux; 302 for (Index k=0; k<dim(); ++k) 303 { 304 if( m_min[k] > p[k] ) 305 { 306 aux = m_min[k] - p[k]; 307 dist2 += aux*aux; 308 } 309 else if( p[k] > m_max[k] ) 310 { 311 aux = p[k] - m_max[k]; 312 dist2 += aux*aux; 313 } 314 } 315 return dist2; 316 } 317 318 template<typename Scalar,int AmbientDim> 319 inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const 320 { 321 Scalar dist2(0); 322 Scalar aux; 323 for (Index k=0; k<dim(); ++k) 324 { 325 if( m_min[k] > b.m_max[k] ) 326 { 327 aux = m_min[k] - b.m_max[k]; 328 dist2 += aux*aux; 329 } 330 else if( b.m_min[k] > m_max[k] ) 331 { 332 aux = b.m_min[k] - m_max[k]; 333 dist2 += aux*aux; 334 } 335 } 336 return dist2; 337 } 338 339 /** \defgroup alignedboxtypedefs Global aligned box typedefs 340 * 341 * \ingroup Geometry_Module 342 * 343 * Eigen defines several typedef shortcuts for most common aligned box types. 344 * 345 * The general patterns are the following: 346 * 347 * \c AlignedBoxSizeType where \c Size can be \c 1, \c 2,\c 3,\c 4 for fixed size boxes or \c X for dynamic size, 348 * and where \c Type can be \c i for integer, \c f for float, \c d for double. 349 * 350 * For example, \c AlignedBox3d is a fixed-size 3x3 aligned box type of doubles, and \c AlignedBoxXf is a dynamic-size aligned box of floats. 351 * 352 * \sa class AlignedBox 353 */ 354 355 #define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix) \ 356 /** \ingroup alignedboxtypedefs */ \ 357 typedef AlignedBox<Type, Size> AlignedBox##SizeSuffix##TypeSuffix; 358 359 #define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \ 360 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \ 361 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \ 362 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \ 363 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \ 364 EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X) 365 366 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int, i) 367 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float, f) 368 EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double, d) 369 370 #undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES 371 #undef EIGEN_MAKE_TYPEDEFS 372 373 } // end namespace Eigen 374 375 #endif // EIGEN_ALIGNEDBOX_H 376
